If two liquids of same volume but different densities $\rho_1$ and $\rho_2$ are mixed,then the density of the mixture is given by:

In the previous problem,if $15.0 \; cm$ of water and spirit each are further poured into the respective arms of the tube,what is the difference in the levels of mercury in the two arms (in $; cm$)? (Specific gravity of mercury $= 13.6$)

Consider two liquids $A$ and $B$ in a $U$-shaped tube in static equilibrium as shown in the figure. If the density of the liquid $A$ is twice the density of liquid $B$,then the relation between $h_A$ and $h_B$ is

An open $U$-tube contains mercury. When $11.2 \,cm$ of water is poured into one of the arms of the tube, how high does the mercury rise in the other arm from its initial level (in $\,cm$)?

Which of the following quantities is expressed as force per unit area?

Consider a vessel filled with a liquid up to height $H$. The bottom of the vessel lies in the $X-Y$ plane passing through the origin. The density of the liquid varies with the $Z$-axis as $\rho(z) = \rho_0 \left[ 2 - \left( \frac{z}{H} \right)^2 \right]$. If $P_1$ and $P_2$ are the pressures at the bottom surface and top surface of the liquid respectively,the magnitude of $(P_1 - P_2)$ is: